Trivium
- For a right triangle, given either the lengths of two sides or the length of one side and measure of one angle, compute the lengths of the remaining sides and the measure of the remaining angles.
- Compute the area of a right triangle.
- For a general triangle, either the lengths of three sides, the lengths of two sides and the measure of an angle, or the lengths of one side and the measure of two angles, compute all possibilities for the lengths of the remaining sides and the measure of the remaining angles.
- For a general triangle, compute its area given the lengths of its sides.
- Given two angles for which the sine and cosine are known compute the sine and cosine for the sum and difference of those angles.
- Given an angle for which the cosine is known compute the sine and cosine of half that angle.
Problems & Challenges
- What is the exact value, expressed in terms of radicals, of \(\cos\Bigl(\frac{\pi}{5}\Bigr)\) and \(\sin\Bigl(\frac{\pi}{5}\Bigr)?\)
- What is a formula, in terms of \(n,\) for \(\cos\Bigl(\frac{\pi}{2^n}\Bigr)?\) What about \(\cos\Bigl(\frac{\pi}{3\times2^n}\Bigr)?\)